fcn farey_len(n){
   var cache=Dictionary();	// 107 keys to 1,000; 6323@10,000,000
   if(z:=cache.find(n)) return(z);

   len,p,q := n*(n + 3)/2, 2,0;
   while(p<=n){
      q=n/(n/p) + 1;
      len-=self.fcn(n/p) * (q - p);
      p=q;
   }
   cache[n]=len;   // len is returned
}